Linked Questions

10
votes
5answers
705 views

Why is $\sqrt{4} = 2$ and Not $\pm 2$? [duplicate]

I've always been told that if $\ x^2 = 4,$ $ =>x = \pm2$ But recently, Prof. mentioned that if $x = \sqrt{4}$, Then $x = +2(only)$ I am very skeptical about this because they both mean the ...
1
vote
4answers
23k views

Is sqrt(x) a function? Does it matter if a domain is given? [duplicate]

Possible Duplicates: Reason why the even root of a number always positive Square roots — positive and negative I saw the following during a practice exam: $f(x) = \sqrt x $ for $x ≥ 2$ ...
-4
votes
4answers
654 views

Why does Wolfram Alpha say that $\sqrt{1}=-1$? [duplicate]

Why does Wolfram Alpha say that $\sqrt{1}=-1$? Is this a mistake or what? Can anyone help? Thanks in advance.
2
votes
3answers
230 views

A question about eliminating square roots [duplicate]

If $\sqrt{x^2} = \pm x$, then why does $\sqrt{(x+2)^2} = x+2$ and not $\pm (x+2)$? This is driving me crazy, so feel free to elucidate. Thanks! ---EDIT--- I'm not sure how the other questions' ...
0
votes
3answers
68 views

Square roots: $ -\sqrt{a} = \sqrt{b}$ [duplicate]

[CLOSED] Thanks GoodDeeds and Henry [1] I understood the fundamental problem. As √9 = ± 3 If , √A = √B Thus, ** ±a = ±b** And so a = b; -a = b; and a = -b;; Thus, √9 = +3 OR -3 Let, √A = ±a ...
0
votes
3answers
91 views

Why does a root only have a positive output? [duplicate]

Let's say I am solving an equation, and end up with this: x^2 = 16 The solutions will be x=4 or x=-4 That makes sense. But when I have this: x = √16 The only solution is x=4 ...
25
votes
2answers
3k views

Significance of $\sqrt[n]{a^n} $?!

There is a formula given in my module: $$ \sqrt[n]{a^n} = \begin{cases} \, a &\text{ if $n$ is odd } \\ |a| &\text{ if $n$ is even } \end{cases} $$ I don't really understand the ...
4
votes
2answers
383 views

Why does the square root of a square involve the plus-minus sign?

If $\sqrt{x^2}$ can be simplified as follows: $\sqrt{x^2} = (x^2)^\frac{1}{2} = x^{\frac{2}{1}\times\frac{1}{2}} =x^\frac{2}{2} = x^1 = x$ Then why would $\sqrt{x^2} = \pm x$?
1
vote
2answers
48 views

Definition of “ the principal n-th root of ” using a sign condition.[modified title]

[ Edited] Is it ok to say that, the principal n-th root of a is simply the number x such that : (1) x to the n-th power is equal to a and (2) x has the same sign as a ? My question deals ...
1
vote
2answers
60 views

Find $f(g(x))=-\sqrt{x}$ where $f(x) =\sqrt {x}$

If we have $f(x)=\sqrt{x}$ Find $g(x)$ where $f(g(x))=-f(x) =-\sqrt{x}$ I know that the square root can have plus and minus value in the same time but I what that $f(g(x))$ value is negative when $...
1
vote
2answers
7k views

Square root of simple binomial function [duplicate]

Let's say I have the following formula: $$\sqrt{a^2-2ab+b^2}=\sqrt{(a-b)^2}=\sqrt{(b-a)^2}$$ When do I know which one of the following I should use?: $$\sqrt{(a-b)^2}=a-b\qquad\text{ or }\qquad \...
0
votes
2answers
83 views

why square root of a positive number is positive? [duplicate]

We have $(+3)^2=(-3)^2=9$. But why do we define $$\sqrt 9=+3?$$ Why $\sqrt9=-3$ is false? Thank you
1
vote
0answers
34 views

Is there an application to NOT assuming that a square root is positive?

Further to the question here:Why is the even root of a number always positive? If it is mere "convention" (agreement) that we use positive real numbers as the even-powered-roots of positive real ...